# Continual Learning of Dynamical Systems in Recurrent Neural Networks through Recyclable Unit Gating

arXiv: https://arxiv.org/abs/2609.38356 · HTML: https://mlsanity.com/paper/2609.38356/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 29 of 29)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Conditional Channel Gated Networks for Task-Aware Continual Learning](https://mlsanity.com/paper/2004.00070/) (2020)
- [Alleviating catastrophic forgetting using context-dependent gating and synaptic stabilization](https://mlsanity.com/paper/1802.01569/) (2018)
- [Continual Learning via Neural Pruning](https://mlsanity.com/paper/1903.04476/) (2019)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [On the difficulty of learning chaotic dynamics with RNNs](https://mlsanity.com/paper/2110.07238/) (2021)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [On Quadratic Penalties in Elastic Weight Consolidation](https://mlsanity.com/paper/1712.03847/) (2017)
- [Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI](https://mlsanity.com/paper/1902.07186/) (2019)
- [Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems](https://mlsanity.com/paper/2207.02542/) (2022)
- [Continual Learning for Recurrent Neural Networks: an Empirical Evaluation](https://mlsanity.com/paper/2103.07492/) (2021)
- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [Bifurcations and loss jumps in RNN training](https://mlsanity.com/paper/2310.17561/) (2023)
- [Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data](https://mlsanity.com/paper/2410.04814/) (2024)
- [Optimal Recurrent Network Topologies for Dynamical Systems Reconstruction](https://mlsanity.com/paper/2406.04934/) (2024)
- [Continual Learning of Dynamical Systems with Competitive Federated Reservoir Computing](https://mlsanity.com/paper/2206.13336/) (2022)
- [Uncovering the Computational Roles of Nonlinearity in Sequence Modeling Using Almost-Linear RNNs](https://mlsanity.com/paper/2506.07919/) (2025)
- [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026)
- [Artificial Neuronal Ensembles with Learned Context Dependent Gating](https://mlsanity.com/paper/2301.07187/) (2023)
- [Continual Learning of Multi-modal Dynamics with External Memory](https://mlsanity.com/paper/2203.00936/) (2022)
- [The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling](https://mlsanity.com/paper/2605.31547/) (2026)

## Abstract (arXiv)

Dynamical Systems Reconstruction (DSR) aims to infer models from observed time series that reproduce a system's qualitative long-term behavior. Continual DSR (cDSR) requires learning new systems while preserving previously learned dynamics, yet even small parameter updates in recurrent models can qualitatively alter their behavior over long autonomous rollouts. We benchmark established continual learning (CL) methods spanning parameter regularization, replay, and parameter isolation on the fully trainable and interpretable Almost-Linear RNN (AL-RNN). Parameter isolation preserves earlier dynamics most effectively, but excessive task-specific allocations can rapidly exhaust a fixed-size network. We therefore introduce Continually-Recyclable Unit-Gating (CRUG), which conserves capacity through compact allocation and forward transfer. Differentiable gates trained with an L0-based penalty select task-specific units, while unused units are recycled for subsequent tasks. Directed connections allow later tasks to reuse earlier representations without affecting the dynamics of previously committed units. CRUG achieves the strongest reconstruction--capacity trade-off among the tested methods with zero forgetting and reliably learns a heterogeneous sequence of nonlinear and chaotic systems. Furthermore, we show that forward transfer is more pronounced and useful when tasks share similar underlying dynamics. Lastly, we demonstrate that CRUG's advantages extend beyond autonomous cDSR to sequential cognitive tasks.